[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2017.25.4.537

SURFACES FOLIATED BY ELLIPSES WITH CONSTANT GAUSSIAN CURVATURE IN EUCLIDEAN 3-SPACE

Ali, Ahmed T. (Department of Mathematics, Faculty of Science, King Abdul Aziz University)
Hamdoon, Fathi M. (Mathematics Department, Faculty of Science, Al-Azhar University)

Publication Information

Korean Journal of Mathematics / v.25, no.4, 2017 , pp. 537-554 More about this Journal

Abstract

In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space ${\mathbf{E}}^3$ . We prove the following results: (1) The surface foliated by an ellipse have constant Gaussian curvature K if and only if the surface is flat, i.e. K = 0. (2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.

Keywords

Surfaces in Euclidean space; Gaussian curvature;

Citations & Related Records

Reference

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